What is the derivative of (1-2x^5(3x-2)^6) ?

The derivative of (1-2x^5(3x-2)^6) is -10(1-2x)^4(3x-2)^6+18(3x-2)^5(1-2x)^5

What is the first derivative of (1-2x^5(3x-2)^6) ?

The first derivative of (1-2x^5(3x-2)^6) is -10(1-2x)^4(3x-2)^6+18(3x-2)^5(1-2x)^5

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Popular >

\frac{d}{d x} ((1 - 2 x)^{5} (3 x - 2)^{6})

- 10 (1 - 2 x)^{4} (3 x - 2)^{6} + 18 (3 x - 2)^{5} (1 - 2 x)^{5}

Solution steps

\frac{d}{d x} ((1 - 2 x)^{5} (3 x - 2)^{6})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (1 - 2 x)^{5}, g = (3 x - 2)^{6}

= \frac{d}{d x} ((1 - 2 x)^{5}) (3 x - 2)^{6} + \frac{d}{d x} ((3 x - 2)^{6}) (1 - 2 x)^{5}

\frac{d}{d x} ((1 - 2 x)^{5}) = - 10 (1 - 2 x)^{4}

\frac{d}{d x} ((3 x - 2)^{6}) = 18 (3 x - 2)^{5}

= (- 10 (1 - 2 x)^{4}) (3 x - 2)^{6} + 18 (3 x - 2)^{5} (1 - 2 x)^{5}

Simplify

= - 10 (1 - 2 x)^{4} (3 x - 2)^{6} + 18 (3 x - 2)^{5} (1 - 2 x)^{5}

2 e^{2 t} + 8 t e^{2 t} + 4 t^{2} e^{2 t}

\frac{d}{d x} (\frac{ln ( x )}{2 x})

\frac{d}{d x} (\frac{6 - 7 x}{2 + x})

x \to 6 - lim (\frac{x ^{6}}{x - 6})

5 x, 2 x^{2}

What is the derivative of (1-2x^5(3x-2)^6) ?
The derivative of (1-2x^5(3x-2)^6) is -10(1-2x)^4(3x-2)^6+18(3x-2)^5(1-2x)^5
What is the first derivative of (1-2x^5(3x-2)^6) ?
The first derivative of (1-2x^5(3x-2)^6) is -10(1-2x)^4(3x-2)^6+18(3x-2)^5(1-2x)^5